PGEs including prostaglandin (hereinafter referred to as PG) E1 and E2 and PGFs including PGF2α are known as metabolites of the arachidonate cascade. For example, PGE2 is known to have cell protection effect, uterine contraction, pain generation effect, promoting peristaltic movement of gastrointestinal tract, arousal effect, gastric secretion inhibition effect, hypotensive effect, diuretic effect and the like.
PGs containing a five-membered ring such as PGEs and PGFs are produced through multiple steps using a so-called Corey lactone as a synthetic intermediate for controlling stereoselectivity at the α side chain group, ω side chain group, hydroxyl group and the like on a five-membered ring, the Corey lactone being a cyclopenta[b]furan-2-one compound which is synthesized from, for example, cyclopentadiene as a starting material through complicated multiple steps including troublesome optical resolution.
These PGs, which are used as pharmacologically active components for pharmaceutical formulations, are required to be produced while controlling undesired potential impurities such as diastereomers and enantiomers.
Therefore, there is a need for producing in good yield an appropriate synthetic intermediate which composes a five-membered ring of PGs in a shorter process than the synthesis process of Corey lactone with excellent stereoselectivity in terms of diastereoselectivity and enantioselectivity.
Meanwhile Non-Patent Literature 1 discloses stereoselective asymmetrical synthesis of bicyclo[3.2.1]octanes by reacting an active methylene of cyclohexanedione carboxylic acid methyl esters with nitroolefins in the presence of quinine alkaloid catalysts by the Michael-Henry reaction to form five-membered rings de novo. This asymmetrical synthesis does not correspond to the production of monocyclic five-membered ring-containing compounds required for production of PGs.
Patent Literature 1 discloses a method for obtaining a product from the Michael reaction of α,β-unsaturated aldehydes and nitroalkanes in the presence of asymmetrical pyrrolidine methanol derivative catalysts. This method does not correspond to the production of cyclic five-membered ring-containing compounds required for production of PGs.    Non-Patent Literature 1: Bin Tan et al., Organic Letters, 2010, vol. 12, p. 2682-2685    Patent Literature 1: Japanese Patent Application Laid-open No. 2009-91257